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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 8 and fixed z and a<0 > For fixed z and a=-25/8, b>=a > For fixed z and a=-25/8, b=37/8





http://functions.wolfram.com/07.23.03.bjfu.01









  


  










Input Form





Hypergeometric2F1[-(25/8), 37/8, 1, z] == (1/(10094175 Pi)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-32 (-1979669 + 23787962 z - 62183352 z^2 + 43609104 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 16 (-1979669 + 23787962 z - 62183352 z^2 + 43609104 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/z) (5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-2018835 + 28302856 z - 79450096 z^2 + 58145472 z^3) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) + (1/(Sqrt[1 - z] z)) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (3364725 - 52450544 z + 195851392 z^2 - 262731392 z^3 + 116290944 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])))










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02